Three-dimensional Numerical Modeling and Computational Fluid

Dynamics Simulations to Analyze and Improve Oxygen Availability

in the AMC Bioartificial Liver

GUY MAREELS ,1 PAUL P. C. POYCK,2 SUNNY ELOOT,1 ROBERT A. F. M. CHAMULEAU,2

and PASCAL R. VERDONCK1

1Cardiovascular Mechanics and Biofluid Dynamics Research Group, Institute of Biomedical Technology, Ghent University,Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium and 2Departments of Experimental Surgery and Hepatology, Academic Medical

Center, University of Amsterdam, Amsterdam, The Netherlands

(Received 15 December 2005; accepted 27 July 2006; published online: 10 October 2006)

Abstract—A numerical model to investigate fluid flow andoxygen (O2) transport and consumption in the AMC-Bioartificial Liver (AMC-BAL) was developed and appliedto two representative micro models of the AMC-BAL withtwo different gas capillary patterns, each combined with twoproposed hepatocyte distributions. Parameter studies wereperformed on each configuration to gain insight in fluid flow,shear stress distribution and oxygen availability in the AMC-BAL. We assessed the function of the internal oxygenator,the effect of changes in hepatocyte oxygen consumptionparameters in time and the effect of the change from anexperimental to a clinical setting. In addition, differentmethodologies were studied to improve cellular oxygenavailability, i.e. external oxygenation of culture medium,culture medium flow rate, culture gas oxygen content (pO2)and the number of oxygenation capillaries. Standard oper-ating conditions did not adequately provide all hepatocytesin the AMC-BAL with sufficient oxygen to maintain O2

consumption at minimally 90% of maximal uptake rate.Cellular oxygen availability was optimized by increasing thenumber of gas capillaries and pO2 of the oxygenation gas bya factor two. Pressure drop over the AMC-BAL andmaximal shear stresses were low and not considered to beharmful. This information can be used to increase cellularefficiency and may ultimately lead to a more productiveAMC-BAL.

Keywords—Computational fluid dynamics, Hepatocyte bio-

reactor, Acute liver failure, Shear stress, Fluid flow, Oxygen

partial pressure, Michaelis–Menten oxygen consumption,

Effective hepatocyte utilization ratio, Internal oxygenation,

External oxygenator.

INTRODUCTION

Acute liver failure (ALF) is a severe disease withhigh mortality rates (60–90%). At present, the onlyefficient therapy is orthotopic liver transplantation(OLT).11 To bridge ALF patients to liver transplan-tation or to regeneration of the native liver, liver sup-port systems are needed. The most promising bridgingmethod for the treatment of ALF patients are bioar-tificial liver (BAL) support systems. These systems areextracorporeal devices that are generally comprised ofa bioreactor in which living hepatocytes are seeded. Ina clinical setting, toxic plasma of ALF patients isperfused through a BAL system and detoxified byviable hepatocytes. A major advantage of BAL sys-tems, as compared to other non-biological liver sup-port systems, is the capacity to provide a full range ofmetabolic functions to compensate for the complexmetabolic disorders seen in ALF. Although many BALsystems have demonstrated their detoxifying capacityor liver-specific functions in in vitro, ex vivo and inphase I clinical studies, no BAL system has shown tosignificantly improve survival in ALF patients bridgedto transplantation in a controlled trial (for review:40).

Important issues for the development of an effectiveBAL system are local plasma flow and oxygen trans-port. Optimal cell function, i.e. detoxifying capacity, isonly obtained when a BAL system is adequately per-fused with plasma to enable efficient mass transfer. Inthis situation, sufficient nutrients (e.g. glucose, fattyacids) and oxygen are supplied, whereas unwantedmetabolites (e.g. ammonia) are efficiently detoxifiedand metabolic end products (e.g. urea, CO2) subse-quently removed. In principle, oxygen (O2) transfer isthe main limitation in the efficiency of a BAL,3 becauseof the low solubility of oxygen in plasma and highdemand for oxygen of functionally active hepatocytes.

Address correspondence to Guy Mareels MScME, Cardiovas-

cular Mechanics and Biofluid Dynamics Research Group, Institute of

Biomedical Technology, Ghent University, Sint-Pietersnieuwstraat

41, 9000 Gent, Belgium. Electronic mail: guy.mareels@ugent.be

Annals of Biomedical Engineering, Vol. 34, No. 11, November 2006 (� 2006) pp. 1729–1744

DOI: 10.1007/s10439-006-9169-6

0090-6964/06/1100-1729/0 � 2006 Biomedical Engineering Society

1729

The AMC-Bioartificial Liver (AMC-BAL; Aca-demic Medical Center, Amsterdam, The Netherlands,patent No: WO 97/12960) was developed with a specialdesign for on-site oxygenation of hepatocytes anddirect contact of plasma to the cells to enhance bidi-rectional solute exchange. The AMC-BAL has shownpromising results in in vitro set-ups, small and largeanimal ALF models, and finally in a phase I clinicalstudy with ALF patients.13,39 But to increase the effi-ciency of the AMC-BAL, further optimization ofplasma perfusion and oxygenation of hepatocytes maybe useful.

Numerical techniques and Computational FluidDynamics (CFD) simulations are useful tools to gaininsight in local flow field and oxygen transport inhollow fiber BALs19,27,30 as well as in other types ofhepatocyte systems.16,23,25 These numerical techniquescan also be used to determine the optimal workingparameters and to further optimize the design of aBAL system. In this respect, we used CFD simulationsas a methodological approach to analyze the configu-ration of the AMC-BAL. We constructed three-dimensional computer models of two representativeunit volumes – micro models – of the laboratory-scaleAMC-BAL. Fluid flow and oxygen transport andconsumption were simulated in these micro models togain insight in the flow field and local cellular oxygenavailability. Numerical parameter studies were per-formed to assess possible improvements in local oxy-gen availability of hepatocytes. Several parameterswere tested: (1) effect of the internal oxygenator sys-tem, (2) pO2 of the oxygenation gas, (3) culture med-ium flow rate, (4) incorporation of an external

oxygenator in the extracorporeal circuit, (5) the num-ber of oxygen capillaries, (6) the effect of plasma per-fusion versus normal culture medium, and (7) the effectof changes of hepatocyte oxygen consumption char-acteristics in time. Finally, we discuss the implicationof this information for the optimization of theAMC-BAL into a more efficient bioartificial liver.

MATERIALS AND METHODS

The internal geometry of the laboratory-scaleAMC-BAL is schematically drawn in Fig. 1 in a lon-gitudinal and transverse cross-section. The bioreactoris built from a cylindrical polycarbonate housing(Fig. 1l) in which two pieces of three-dimensional (3D)non-woven polyester matrix mat (Fig. 1e, g) are spi-rally wound around a massive inner core (Fig. 1i). Aspace between the two mat segments (Fig. 1f) is leftopen for an additional hepatocyte seeding port (notshown). In the hydrophilic matrix, high-density hepa-tocyte culture is possible. Between the matrix windings,hydrophobic gas capillaries (Fig. 1m) are positioned inparallel along the entire bioreactor as an internaloxygenator system to supply additional oxygen to thehepatocytes. Culture gas (95% air, 5% CO2) is perfusedthrough these capillaries. Plasma enters the bioreactorthrough an inlet port (Fig. 1b) and flows through theinflow zone (Fig. 1j) further passes the hydrophilicmatrix mat and through the void inter-capillary space(Fig. 1n). Plasma exits the bioreactor via the outflowzone (Fig. 1k) through the outlet port (Fig. 1d).Plasma and culture gas are counter-current flows.

FIGURE 1. Longitudinal (left) and transverse (right) view of the internal geometry of the AMC-BAL with a – gas outlet; b – gasinlet; c – plasma inlet port; d – plasma outlet port; e – first mat segment; f – interspace; g – second mat segment; h – polyurethanepotting to separate gas and fluid compartment; i – inner core; j – inflow zone; k – outflow zone; l – polycarbonate housing; m – gascapillaries; n – inter-capillary space through which plasma flows. The inline and triangular micro models are designated.

MAREELS et al.1730

Computer Model

Since the entire BAL geometry is too large andcomplex to model, three-dimensional unit volumes –micro models – were isolated from the geometry(Fig. 1). Each three-dimensional micro model (Fig. 2)consists of 2 pieces of mat (thickness = 400 lm,height = 1563 lm, length = 50 mm; Fig. 1e, g) sepa-rated by a void interspace section (length = 6 mm;Fig. 1f). At both sides of the mat, gas capillaries (outerdiameter = 380 lm) and an inter-capillary space arepresent. The two micro models differ only in their gascapillaries’ position. Either the capillaries are in a rect-angular (inline micro model – Fig. 2) or in a triangular(triangular micro model – Fig. 2) pattern. These twoconfigurations are the most distinct that could be iso-lated as the position of the capillaries relative to eachother changes continuously along the course of thespiral mat (Fig. 1). These two micro models weretherefore considered to be representative for the entireAMC-BAL. Simulations on both models will allow usto assess the influence of the capillary arrangement.

Both models were created in the modeling softwareGambit 2 (Fluent Inc., Sheffield, UK). All dimensionswere derived from a laboratory-scale AMC-BAL orwere supplied by the manufacturer. The curvature ofthe mat was neglected and the inflow and outflowzones before and after the mat segments in the AMC-BAL were not included in the micro models. Eachstandard micro model contains the equivalent capillary

wall surface of 1 whole capillary. Since the entire lab-oratory-scale AMC-BAL contains 300 capillaries, eachmicro model can thus be considered as 1/300th part ofAMC-BAL. Consequently, one AMC-BAL can beregarded as a combination of 300 separate micromodels in parallel.

Modeling Fluid Flow

Theoretical Model

To simulate fluid flow, the commercial CFD packageFluent 6.2 (Fluent Inc., Sheffield, UK) was used tonumerically solve the steady-state Navier–Stokes equa-tions. Standard pressure discretization scheme and sec-ond order upwind momentum discretization schemewere used. Pressure–velocity coupling scheme wasSIMPLE. Fluid properties were set to those of culturemedium to allow future validation with in vitro experi-ments. Culture medium was modeled as an incom-pressible, isothermal,Newtonian fluid composed of 90%water (q = 998 kg/m3) and 10% serum (q = 1030 kg/m3) with a resulting density of 1001.2 kg/m3. Dynamicviscosity l of culture medium with 5 g/l bovine serumalbumin (BSA) at 37�Cwas set to 0.691 mPa s.26 Plasmaviscosity at 37�C was set to 1.3 mPa s.31

Resistance to Flow of the Non-woven Polyester Mat

The non-woven polyester matrix was modeled as anisotropic homogeneous porous zone. A measure for theviscous resistance of the non-woven polyester matrixused in Fluent 6.2 was determined in an experimentalset-up by establishing the pressure drop – flow raterelationship. A sample of this matrix fabric sheet wasclamped between two connecting tubes. These tubeswere placed in a closed circuit with an overflow reser-voir, which provided a constant static pressure load overthe matrix sample. Pressure difference over the matrixsheet was measured using a calibrated differential pres-sure transducer (Fuji Electrics FCX, Japan). Flow ratewas measured gravimetrically. De-ionized water wasused. Static pressure load was set so average velocities inthe experiment were in the same order of magnitude ascould be expected in the AMC-BAL (1–7 mm/s). Aviscous resistance factor of 2.7±0.2� 1010 m)2 wascalculated as an average of 10measurements. Resistanceto flow of hepatocyte cell layers (section ‘‘Modelingoxygen transport and consumption’’) was modeledusing the same viscous resistance factor.

Boundary Conditions

We assumed that total flow rate (15 ml/min) insidethe research scale AMC-BAL is homogenously dis-tributed. In this way, each micro model has the same

FIGURE 2. AMC-BAL micro models. Upper left, inline micromodel; upper right, triangular micro model (c – capillary wall, M– non-woven matrix mat, f – inter-capillary space); lower left,inline micro model with double number of capillaries; lowerright, triangular micro model with double number of capillaries.

Improving Performance of the AMC-BAL Using CFD 1731

flow rate of 0.05 ml/min, i.e. 1/300th of the total flowrate. Pressure inlet boundary conditions were used;outlet boundary condition was a zero pressure outflow;the capillary walls were ,no-slip’ walls and symmetryboundary conditions were used at the side walls of themodel.

Modeling Oxygen Transport and Consumption

Theoretical Model

To simulate oxygen transport and consumption,Fluent 6.2 solves the steady-state convection–diffusion-reaction equation (Eq. 1). Discretization scheme wasset to QUICK.

@

@xiðqui/� qD

@/@xiÞ ¼ S/ ð1Þ

The transported scalar / is the local oxygen con-centration (vol.%), which is also the product of theoxygen solubility a and the local oxygen partial pres-sure (pO2) according to Henry’s Law (/ = a*pO2).Oxygen solubility a is 3.1385� 10)5 ml O2/mmHg*mlfluid in culture medium and 2.855� 10)5 ml O2/mmHg*ml fluid in plasma. D is the oxygen diffusioncoefficient, which is 2.92� 10)9 m2/s in culture med-ium and 2.18� 10)9 m2/s in plasma.2,17,33,44 Oxygenconsumption by the primary porcine hepatocytes in theAMC-BAL was modeled by an additional source termS/, which was only implemented in regions that weredesignated to contain hepatocytes.

S/ ¼ �qVMqcell

//þ aKM

ð2Þ

This source term (Eq. 2) was based on the Micha-elis–Menten kinetics of O2 consumption by hepato-cytes. As such, O2 uptake is dependent on the localhepatocyte density qcell and in a non-linear waydependent on the local O2 availability.

Michaelis–Menten parameters of primary porcinehepatocytes were obtained from Balis et al.1 Values ofculture day 2 were taken as they are characterized by ahighly demanding O2 uptake (VM = 0.7286 nmol/s*106 cells; KM = 2 mmHg). These values were mea-sured in 2D culture, whereas hepatocyte culture in theAMC-BAL is three-dimensional and at high density.For this reason, a lower O2 consumption may be ex-pected as the specific O2 uptake rate per cell is reportedto decrease at increasing cell densities.30 On the otherhand, O2 consumption may rise significantly when ametabolic load is applied to the cells.4 As such, theproposed consumption characteristics are justified byassuming these values to represent the most limitingcase for oxygen availability. Consequently, attention

must be paid when comparing simulation results toother numerical studies.19,23,25

Hepatocyte Distribution in the Micro Models

In an in vitro setting, the laboratory scale AMC-BAL is seeded with 1 billion porcine hepatocytes viathree different loading ports, while gently rotating thebioreactor to assure a homogeneous cell distribution.As we assumed that one micro model is one 300th partof an entire laboratory scale AMC-BAL, one micromodel contained 3.33 million cells.

Since no detailed information on the internalhepatocyte distribution in the AMC-BAL is available,two cell distributions are hypothesized. In cell distri-bution 1, all hepatocytes are homogeneously distrib-uted in the non-woven matrix (resulting hepatocytedensity qcell of 53.7� 106 cells/ml). In previous mac-roscopic and microscopic studies of an early prototypeAMC-BAL, the majority of the hepatocytes wereimmobilized within the three-dimensional matrix.14

However, given the undifferentiated method of hepa-tocyte seeding, it is possible that hepatocytes also ad-here to the surface of gas capillaries. Therefore, in celldistribution 2, 50% of the hepatocytes are located inthe matrix (qcell = 31.7� 106 cells/ml) and 50% in ahepatocyte layer around the capillaries. The hepato-cyte layer was set to be 122 lm, with a qcell of81.7� 106 cells/ml. This cell layer thickness is in therange of what is used in other numerical studies19,20

and is consistent with the size of primary porcinehepatocyte 3D cell clusters found in vitro.15 All pro-posed cell densities were also considered to be realis-tic.8,21,37

The complete AMC-BAL cannot be modeled byusing only one cell distribution or only one micromodel. Therefore, each cell distribution was applied toboth micro models, leading to four basic configura-tions in total. All four micro model configurationswere assessed independently. With a combination ofthese micro models, the entire AMC-BAL can bemodeled in future studies.

O2 Diffusion Constant Through Non-woven Matrix

Free O2 diffusion through the mat zone is hinderedby the non-woven arrangement of hydrophilic polyes-ter fibers, which are considered to be impermeable toO2. To compensate for this hindered diffusion, a cor-rection factor for the O2 diffusion coefficient in the matvolume was determined.

On a microscopic view of the non-woven matrix, themat porosity was determined to be 91%. A modifiedtwo-dimensional inline micro model was constructedwith 250 polyester fiber circles randomly located withinthe boundaries of the mat volume. On this modified

MAREELS et al.1732

inline micro model, the pO2 distribution was simulatedusing hepatocyte distribution 1 (Fig. 3A). Standardboundary conditions were used and culture flow rate waszero. O2 diffusion coefficient in the mat zone of themodified micro model was the same as for free culturemedium, since culture medium occupies the void spacesbetween the polyester fibers. Subsequently, an analogoussimulation was performed on a regular inline micromodel, i.e. with the mat modeled as homogeneousmedium, with an adjusted O2 diffusion coefficient in themat zone to match the results of the ,modified’ model(Fig. 3B). A correction factor of 0.85(Dmat = 2.48� 109 m2/s) for O2 diffusion was necessaryto take into account the presence of the non-wovenpolyester matrix mat. This correction factor is in

accordance with the equation of Rayleigh (correction

factor � 1�solid fraction1þsolid fraction ¼ 0:835), which has been experi-

mentally verified for various sheets of porous

media.29,32,34

O2 Diffusion Constant Through Zones ContainingHepatocytes

Oxygen can diffuse through both continuous fluidspaces as well as through hepatocytes. In regionsseeded with hepatocytes, the resulting ‘‘effective’’ dif-fusion coefficient Deff will be lower than in free me-dium, since O2 diffuses more slowly throughhepatocytes. The extent to which the diffusivity isreduced will logically depend on the local hepatocyte

density. Since experimental data on O2 diffusionconstants through hepatocyte cell layers with differentcell densities is not readily available, a theoreticalapproach was chosen.

Riley et al.35 developed an empirical relation (Eq. 3)that relates the effective diffusion coefficient Deff to thelocal free diffusion coefficient D0, the intracellular dif-fusion coefficient Dcell and the cell volume fraction /.This equation, based on Monte Carlo simulations,shows a good agreement with available data through-out a wide range of cell volume fractions (0.04</<0.95).

Deff

D0¼ 1� ð1�Dcell

D0Þð1:727/� 0:8177/2 þ 0:09075/3Þ

ð3Þ

Dcell was set to 0.25� 10)9 m2/s, which is an average ofintracellular O2 diffusion constants in hepatocytes re-ported by Jones.22 Cell volume fraction / is the localvolume percentage of space that is occupied by he-patocytes and was calculated as the product of thelocal hepatocyte cell density and the average hepato-cytes cell volume.9 Local free diffusion coefficient D0 isdependent on the perfusion fluid, e.g. culture mediumor plasma, and on the location of hepatocytes in themodel; either in the inter-capillary space or in the matzone. O2 diffusivities in different regions of both micromodels are presented in Table 1.

The obtained local diffusion coefficients are in therange of reported values for hepatocytes and other celltypes.6,16,18,41,43

Boundary Conditions

Oxygen partial pressure (pO2) of incoming culturemedium was set to 146.5 mmHg, which was an averageof three culture medium pO2 measurements using anABL505 blood-gas analyzer (Radiometer Copenha-gen). Axial and radial O2 transport resistances in gascapillaries were neglected, since the culture gas flowrate through the gas capillaries and their O2 perme-ability are high.5 As such, O2 supply through gascapillaries was modeled by imposing a constant150 mmHg pO2 on the capillaries’ outer walls, whichcorresponded to the pO2 of culture gas used in vitro(95% air, 5% CO2). All other boundary faces haveno-flux boundary conditions.

Grid Dependency

One micro model mesh contained approximately3.75 million finite volume mesh elements. Furtherincrease in the number of cells rendered identicalsimulation results.

FIGURE 3. Determination of the correction factor for O2 dif-fusion through the non-woven polyester mat. (A) pO2 distri-bution [mmHg] on modified inline micro model (polyesterfibers drawn) under standard boundary conditions, no med-ium flow; (B) identical pO2 distribution [mmHg] obtained withidentical simulation settings, but with mat as homogeneousmedium with an adjusted diffusion constant (with a factor of0.85) to account for hindered diffusion.

Improving Performance of the AMC-BAL Using CFD 1733

Simulations Overview and Assessment

As previously stated, four micro model configura-tions were used: (a) the inline micro model with celldistribution 1, (b) the inline micro model with celldistribution 2, (c) the triangular micro model with celldistribution 1, and finally (d) the triangular micromodel with cell distribution 2. Fifteen case studies(Table 2) were performed on each configuration.

The first case study was simulated using standardboundary conditions as described in previous para-graphs. This ,reference case’ study (1) is the internalcontrol for all other case studies with the same micromodel configuration. The effect of the internal oxy-genation system was assessed by disabling culture gas

flow (2), and by assessing the effect of an externaloxygenator that oxygenates incoming medium to adoubled pO2 as an alternative for internal oxygenation(3). To increase oxygen availability to the hepatocytes,different strategies were assessed. First, by using a moreoxygen rich culture gas, i.e. a doubled pO2 gas (4) orcarbogen gas (95% O2) (5). Second, by incorporating anexternal oxygenator to increase incoming medium pO2

to a doubled (6) or carbogen (7) level. Third, bychanging culture medium flow rate to a doubled (8) or10-fold (9) flow rate. Finally, by doubling the numberof capillaries (10) or by combining the double numberof capillaries with a doubled culture gas pO2 (11). Incases with a doubled number of capillaries, cell density

TABLE 1. O2 diffusion constants in different zones of the micro models.

Region in the micro model

D0 [10)9 m2/s]qcell[106 cells/ml] /

Deff

D0

Deff [10)9 m2/s]

Cult. med. Plasma Cult. med. Plasma

No hepatocytes

Inter-capillary space 2.92 2.18 0 0 1 2.92 2.18

In mat 2.48 1.85 0 0 1 2.48 1.85

Cell distribution 1

In mat 2.48 1.85 53.7 0.172 0.75 1.87 1.41

Cell distribution 2

In mat 2.48 1.85 31.7 0.102 0.85 2.11 1.59

In hepatocyte cell layer around capillaries –

part in mat zone

2.48 1.85 81.7 0.262 0.64 1.59 1.22

In hepatocyte cell layer around capillaries –

part in inter-capillary space

2.92 2.18 81.7 0.262 0.64 1.86 1.41

The ratio of the effective diffusion constant to the free diffusion constant Deff/D0 is calculated from the local free oxygen diffusion constant D0

and the local cell volume fraction / using Eq. 3. The local effective diffusion coefficients Deff in culture medium and plasma per region are

presented in the last column.

TABLE 2. Overview of simulations.

Case Fluid pO2 gas (mmHg) pO2 medium (mmHg) Qmedium (ml/min) # capillaries KM (mmHg)

Reference case

(1) Standard boundary conditions Culture medium 150 146.5 0.05 1 2

Effect of the internal oxygenator

(2) pO2 gas = 0 Culture medium 0 146.5 0.05 1 2

(3) pO2 gas = 0; pO2 medium� 2 Culture medium 0 293 0.05 1 2

Increasing oxygen availability

(4) pO2 gas�2 Culture medium 300 146.5 0.05 1 2

(5) pO2 gas = carbogen Culture medium 722 146.5 0.05 1 2

(6) pO2 medium�2 Culture medium 150 293 0.05 1 2

(7) pO2 medium = carbogen Culture medium 150 722 0.05 1 2

(8) Fluid flow rate Qmedium� 2 Culture medium 150 146.5 0.10 1 2

(9) Fluid flow rate Qmedium� 10 Culture medium 150 146.5 0.50 1 2

(10) No. capill. �2 Culture medium 150 146.5 0.05 2 2

(11) No. capill. �2; pO2 gas� 2 Culture medium 300 146.5 0.05 2 2

Clinical versus experimental setting

(12) Plasma Plasma 150 146.5 0.05 1 2

(13) Plasma; pO2 gas� 2 Plasma 300 146.5 0.05 1 2

Changes of hepatocyte O2 consumption in time

(14) KM day 4 Culture medium 150 146.5 0.05 1 4.75

(15) KM day 5 Culture medium 150 146.5 0.05 1 7.5

Each case is applied to the four basic micro model configurations (inline and triangular micro model each with cell distribution 1 or 2).

MAREELS et al.1734

in the hepatocyte layer around the capillaries was keptconstant. This lead to a cell layer thickness of 68 lm,keeping the number of hepatocytes around all capil-laries equal to 50% of total, as was initially proposed. Inmicro models with double number of capillaries thedistance between the capillaries is halved (see Fig. 2).

In the next case studies, we studied the effect ofplasma versus culture medium, since this is the maindifference in perfusion in a clinical setting as comparedto an experimental setting. Standard boundary condi-tions (12) and a doubled pO2 gas (13) were used andcompared with cases (1) and (4). Finally, time-relatedchanges in oxygen consumption characteristics ofhepatocytes were investigated by varying KM values.KM values of culture day 4 (14) and 5 (15) werecompared to the reference case (1). According to Baliset al.,1 KM values change remarkably throughout thefirst 5 days, whereas VM values remain constant. Wetherefore kept VM constant in these simulations.

The proposed simulation cases on the four differentmicro model configurations were assessed by examin-ing pO2 distributions. However, not every simulatedpO2 profile can be shown due to brevity reasons. Toevaluate the effect of the parameters discussed in theparameter study, the local effective hepatocyte utiliza-tion ratio Vratio (Eq. 4) was studied.30

Vratio ¼/

/þ aKMð4Þ

Vratio is the ratio of the observed oxygen consump-tion rate to the maximal hepatocyte oxygen consump-tion rate, i.e. VM, and ranges between 0 and 1(asymptotically). A threshold for Vratio of 0.9 was cho-sen as introduced by Patzer30 and corresponds with aminimal pO2 level of 18 mmHg when KM = 2 mmHg.Consequently, oxygen availability in the AMC-BAL was quantified by determining the percentage ofhepatocytes with Vratio>0.9.

RESULTS

Fluid Flow and Shear Stress Distribution

Figure 4 represents an example of colorimetriccontour plots of fluid flow and shear stress distributionsin two different micro models with different hepatocytedistributions. In the upper part, velocity magnitudes(m/s, left legend) in a transverse plane midway throughthe first mat segment are shown for the reference case(case 1) of an inline micro model with hepatocyte dis-tribution 1 (Fig. 4A1) and for a triangular micro modelwith hepatocyte distribution 2 and with a doublenumber of capillaries (case 10–11) (Fig. 4B1). The

contour plots can be mirrored with respect to the hor-izontal axis as micro models are symmetrical.

Fluid flows in the non-woven matrix mat zone andin the hepatocyte cell layers were orientated axiallyand are uniform in size (approx. 8 lm/s in Fig. 4A1and 37 lm/s in Fig. 4B1). In the inter-capillary space,flow velocities have a poiseuille-like (parabolic) profilewith maximal velocities of approx. 3.6 mm/s inFig. 4A1 and 7.8 mm/s in Fig. 4B1. In the interspacebetween two mat segments, flow lines expand radiallydue to the sudden increase in local cross-sectional area.However, these flow lines reconverge when entering thesecond mat segment, where the velocity profile wasidentical compared to the first mat segment (notshown). Static pressure drop over the entire micromodel was 15.7 Pa in the reference case of the inlinemicro model with hepatocyte distribution 1 (Fig. 4A)and 69.3 Pa for the triangular micro model withhepatocyte distribution 2 and double number of cap-illaries (Fig. 4B). The lower parts of Fig. 4 (A2 and B2)show corresponding shear stress distributions (Pa,right legend). Maximal shear stresses were generallylocated near the mat side surfaces and also – in case ofcell distribution 2 – at the boundary between thehepatocyte cell layer and inter-capillary space.

In Table 3, an overview is given of maximumvelocity magnitudes in the inter-capillary space, uni-form velocity magnitudes in the mat/hepatocyte layerzone, as well as static pressure losses over the entiremicro model and maximal local shear stresses for allsimulation cases. Maximum velocities in the inter-capillary space ranged between 3.6 and 45 mm/s,whereas uniform velocities in the mat/hepatocyte layerranged between 8 and 110 lm/s. Simulation resultsshowed that velocities in the mat zone and in hepato-cyte layers were consistently two orders of magnitudesmaller than in the inter-capillary space. Velocityprofiles and shear stress profiles were similar for thedifferent simulation cases, but differed in magnitudebetween cases when flow rate was altered or when theinternal geometry had been changed, e.g. due toadditional gas capillaries and/or hepatocyte layersaround the capillaries. Static pressure loss over theentire micro model and local shear stress levels wereadditionally influenced by the type of fluid, e.g. plasmaor culture medium. Static pressure loss over the entiremicro model ranged from approx. 16 to 203 Pa.Maximum shear stress ranged between approx. 0.03and 0.40 Pa. Largest maximum values were reached inhepatocyte distribution 2 with a 10-fold flow rate.

Importantly, both the inline and triangular micromodel had the same flow field, static pressure loss andshear stress distributions within a simulation case withcertain boundary conditions and hepatocyte distribu-tion (comparison not shown).

Improving Performance of the AMC-BAL Using CFD 1735

Oxygen Transport and Consumption

Results of oxygen transport and consumption si-mulations are presented by means of two contour plotsof pO2 and Vratio distributions (Fig. 5). Also, Table 4presents detailed information for each simulated caseand micro model configuration on the percentage ofhepatocytes that consume oxygen at a minimal Vratio

level of 0.9.

Reference Case Simulations (Case 1)

Figure 5A1 illustrates the pO2 distribution in atransverse plane midway through the first mat segmentin the reference case (case 1) for the inline micromodel with hepatocyte distribution 1. Highest pO2

(150 mmHg) was found close to the capillary wall.A large pO2 gradient extended radially from thecapillary and was steeper at the side of the capillary in

FIGURE 5. Colorimetric contour plot of pO2 (mmHg, left legend, upper part 1) and effective hepatocyte utilization ratio Vratio

(dimensionless, right legend, lower part 2) in a transverse plane midway through the first mat segment, in the reference case (case1) of an inline micro model with hepatocyte distribution 1 (A1 and A2 resp.) and in a triangular micro model with hepatocytedistribution 2 and with double number of capillaries and doubled culture gas pO2 (case 11) (B1 and B2 resp.) (Note: B1 differentscale compared to A1).

FIGURE 4. Colorimetric contour plot of velocity magnitudes (m/s, left legend, upper part 1) and shear stress levels (Pa, rightlegend, lower part 2) in a transverse plane midway through the first mat segment, in the reference case (case 1) of an inline micromodel with hepatocyte distribution 1 (A1 and A2 resp.) and in a triangular micro model with hepatocyte distribution 2 and withdouble number of capillaries (case 10–11) (B1 and B2 resp.).

MAREELS et al.1736

the mat zone. At a radial distance of 86 lm from thecapillary, pO2 in the mat zone dropped already below20 mmHg. A region where oxygen was depleted(0 mmHg) is present in the center of the hepatocyte-seeded mat throughout both mat zones. AnalogouspO2 distributions were found in cross-sections of themicro model further downstream to the plane ofFig. 5A1, but with overall decreasing average oxygenlevel. Oxygen content of the perfused culture mediumin the inter-capillary space dropped from its initialvalue of 146.5 mmHg to approx. 60 mmHg midwaythe first mat segment and further decreased down-stream to 28 mmHg at the end of the first mat segment.At the start of the second mat segment, culture med-ium pO2 in the inter-capillary space was increased to40 mmHg and again decreased to 22 mmHg at the endof the mat segment.

As a standard for cellular oxygen availability, theeffective hepatocyte utilization ratio Vratio was calcu-lated (Fig. 5A2). Complying with pO2 distribution,hepatocytes in the center of the mat zone cannotconsume oxygen at all (Vratio� 0), whereas hepatocytesclosest to the capillaries have enough oxygen availableto consume oxygen at near maximum capacity(Vratio� 1). Approximately 16% of all hepatocytes inthe model consumed oxygen with Vratio>0.9 (Ta-ble 4). A change to hepatocyte distribution 2 wascharacterized by a larger radial pO2 gradient aroundthe capillaries and a more extended zone of zero oxy-gen content in the mat segments. Due to the additionalpresence of a dense hepatocyte layer around the cap-illary, pO2 dropped below 20 mmHg from a radialdistance of 65 lm from a capillary (compare to 86 lm

in hepatocyte distribution 1). Nevertheless, 29% of allhepatocytes attained a Vratio of more than 0.9. Fiftyfour percent of the hepatocytes in cell layers aroundthe capillaries reached the threshold of Vratio>0.9,whereas 3% of the hepatocytes in the mat zone.

pO2 and Vratio distributions for the reference case ofthe other three micro model configurations are notshown for brevity reasons.

Simulation results also showed that inline and tri-angular micro models, using the same hepatocyte dis-tribution, showed qualitative and quantitative identicalpO2 distributions.

The Effect of the Internal Oxygenator (Case 2,3)

Disabling culture gas flow (�pO2 gas = 0 – case 2)led to a reduction of cells with Vratio>0.9 to approxi-mately 2% for all micro model configurations. Replac-ing the internal oxygenator by an external oxygenator,which doubles culture medium pO2 (case 3), led to a‘‘Vratio>0.9’’ fraction of approx. 6% for all micromodel configurations. More specifically, in cell distri-bution 2, this was true for only 1% and 2% of thehepatocytes around the capillaries, and for 3% and11%of the hepatocytes in the mat zone, for case 2 and 3,respectively.

Increasing Oxygen Availability (Case 4–11)

Doubling culture gas pO2 (case 4) almost doubled‘‘Vratio>0.9’’ percentages (Table 4) from approxi-mately 16% to 30% in micro models with hepatocytedistribution 1; an increase of 93%. A 75% increase(29–50%) was obtained in micro models with cell

TABLE 3. Overview of the maximum velocity in the inter-capillary space, the uniform velocity in the mat/hepatocyte layer zone,the static pressure loss over the entire model and the maximal shear stress for all simulation cases and for different hepatocyte

distributions.

Cases Hepatocyte distr. 1 Hepatocyte distr. 2

Velocity in mat/hepatocyte cell layer (mm/s) – Maximum velocity in inter-capillary space (mm/s)

(1,2,3,4,5,6,7,14,15) Standard flow rate 0.0085 – 3.59 0.011 – 4.60

(8) Qmedium� 2 0.017 – 7.17 0.022 – 9.20

(9) Qmedium� 10 0.084 – 35.7 0.11 – 45.0

(10,11) No capillaries�2 0.0195 – 5.69 0.037 – 7.75

(12,13) Plasma 0.0085 – 3.59 0.011 – 4.60

Static pressure loss over micro model (Pa)

(1,2,3,4,5,6,7,14,15) Standard flow rate 15.7 20.6

(8) Qmedium� 2 31.4 41.1

(9) Qmedium� 10 155.7 203.3

(10,11) No capillaries�2 36.1 69.3

(12,13) Plasma 30.0 39.3

Maximum shear stress (Pa)

(1,2,3,4,5,6,7,14,15) Standard flow rate 0.032 0.041

(8) Qmedium� 2 0.064 0.083

(9) Qmedium� 10 0.31 0.40

(10,11) No capillaries�2 0.056 0.083

(12,13) Plasma 0.057 0.073

Values for the inline and triangular micro model are identical.

Improving Performance of the AMC-BAL Using CFD 1737

distribution 2. This increase mainly occurred in thehepatocyte layer around capillaries, i.e. 55% in case 1to 95% in case 4. A further pO2 gas increase tocarbogen level (case 5) led to an approximate qua-druple and triple ‘‘Vratio>0.9’’ fraction compared tothe reference case for distribution 1 and 2, respec-tively. In the latter, hepatocytes in both the mat zoneas well as in the cell layers have increased thresholdpercentages. Furthermore, about 7% more hepato-cytes attained the threshold in the triangular capillaryarrangement compared to inline when using hepato-cyte distribution 2. In distribution 1, inline and tri-angular configurations rendered quasi-identicalresults.

Doubling culture medium pO2 (case 6) led to a 28%and 20% increase in Vratio percentages for cell distri-bution 1 and 2, respectively. In the latter, the relativeincrease was higher in the mat zone as compared to thehepatocyte layers. Further increase of pO2 medium tocarbogen level (case 7) led to a 125% and 88% increasein ‘‘Vratio>0.9’’ percentages compared to the refer-ence case for distribution 1 and 2, respectively. Inlineand triangular models rendered identical results underthe same hepatocyte distribution.

Doubling culture medium flow rate (case 8) resultedin a 14% and 10% increase in ‘‘Vratio>0.9’’ fractionfor distribution 1 and 2, respectively. Further increaseof culture medium flow rate up to a 10-fold (case 9)

TABLE 4. Percentages of total hepatocyte cell amount that attain a Vratio > 0.9.

% Hepatocytes with Vratio > 0.9

Case Hepatocyte distribution 1 Hepatocyte distribution 2

Inline (%) Triangular (%) Inline (%) Triangular (%)

Mat (%) Capill. (%) Mat (%) Capill. (%)

Reference case

(1) Standard boundary conditions 15.7 15.8 28.8 28.6

3.3 54.1 3.3 53.5

The effect of the internal oxygenator

(2) pO2 gas = 0 1.7 1.7 1.7 1.7

3.1 0.4 3.1 0.4

(3) pO2 gas = 0; pO2 medium� 2 6.2 6.2 6.3 5.9

11.0 1.7 10.3 1.7

Increasing oxygen availability

(4) pO2 gas�2 30.4 30.2 50.3 50.3

5.1 95.1 5.0 94.9

(5) pO2 gas = carbogen 62.4 64.5 80.7 88.3

61.2 100.0 76.3 100.0

(6) pO2 medium�2 20.1 20.2 34.5 33.9

11.8 57.0 11.0 56.5

(7) pO2 medium = carbogen 35.5 35.1 54.2 53.4

40.6 67.7 37.5 69.1

(8) Qmedium� 2 17.9 18.1 31.6 31.4

6.6 56.4 6.5 56.0

(9) Qmedium� 10 28.4 28.6 45.7 45.6

22.2 68.9 22.1 68.9

(10) No capillaries�2 31.8 31.8 56.7 56.8

14.1 100.0 14.3 100.0

(11) No capillaries�2; pO2 gas�2 61.0 59.9 87.5 84.8

75.3 100.0 69.9 100.0

Clinical versus experimental setting

(12) Plasma 12.0 12.0 22.9 23.0

2.6 43.0 2.6 43.0

(13) Plasma; pO2 gas� 2 22.8 22.9 40.8 40.9

2.9 78.4 2.9 78.3

Changes in hepatocyte O2 consumption in time

(14) KM day 4 8.7 8.7 18.9 18.9

1.1 36.4 1.1 36.4

(15) KM day 5 5.0 5.1 12.9 13.0

0.3 25.3 0.3 25.5

In the case of hepatocyte distribution 2, distinction is made between the percentage of the total number of hepatocytes in the mat and the

percentage of total number of hepatocytes in the cell layers around the capillaries.

MAREELS et al.1738

resulted in an 81% and 59% increase for distribution 1and 2, respectively. Typically in cases with increasedflow rate in cell distribution 2, Vratio percentages in themat zone changed remarkably, whereas in the hepa-tocyte layers there was only a minor increase. Again,inline and triangular models rendered identical resultsunder the same hepatocyte distribution.

A 2-fold increase in the number of capillaries (case10) resulted in a doubled percentage of cells that attainthe Vratio>0.9 threshold in cell distribution 1(+102%) and 2 (+98%). In the latter, this increaseoccurred in the mat zone as well as in the cell layeraround the capillaries. The combination of a doublenumber of gas capillaries and a doubled pO2 gas (case11) increased the threshold percentages to almostquadruple (+280%) for cell distribution 1 and triple(+200%) for cell distribution 2. Again, only minordifferences existed between inline and triangular micromodels.

Figure 5B1 shows the pO2 distribution in a trans-verse plane midway through the first mat segment inthe triangular micro model with cell distribution 2(case 11). In this case, highest pO2 levels (�300 mmHg)were only found close to the capillary walls. A verysteep radial gradient was noted in the hepatocyte celllayer around the capillaries. pO2 in the center of themat zone was 7 mmHg. As in the reference case, pO2

distributions of cross-sections further downstreamshowed analogous results as compared to Fig. 5A1,but with overall decreasing average oxygen level. Thedistribution of Vratio corresponding to the pO2 distri-bution of case 11 is depicted in Fig. 5B2. The entirehepatocyte layer (100%) around the capillaries andlarge parts of the mat zone (70%) had a Vratio of atleast 0.9. Consequently in case 11, 85% of all hepato-cytes had a Vratio higher than 0.9 (Table 4).

Clinical Versus Experimental Setting (Case 12,13)

Changing fluid properties from culture medium toplasma resulted in a 24% decrease in Vratio>0.9 per-centages in micro models with cell distribution 1 and a20% decrease in cell distribution 2 (case 12). DoublingpO2 gas in the clinical setting (case 13) showed a relativerise of 91% and 78% compared to the clinical referencecase (case 12) in cell distribution 1 and 2, respectively.Compared to the analog case in in vitro settings (case4), the change of fluid properties also corresponds witha respective 25% and 19% decrease of the‘‘Vratio>0.9’’ fraction.

Changes in Hepatocyte O2 Consumption in Time (case14,15)

Changing KM values to the situation on day 4 (case14) or 5 (case 15) causes slight increases in absolute

pO2 level. Also, pO2 gradients are less steep and theoxygen depleted zone in the center of the matrix isslightly smaller (not shown). However, ‘‘Vratio>0.9’’fractions decreased 45% and 68% for cell distribution 1and 34% and 55% for distribution 2 compared to day 2(case 1) for day 4 and 5, respectively.

DISCUSSION

Fluid Flow and Shear Stress Distribution

Perfusion of a micro model was largely influencedby the presence of the non-woven mat. Although thecross-sectional area of the inter-capillary space and thenon-woven mat are roughly the same size, fluid flow inthe mat zone was generally two orders of magnitudesmaller as compared to the flow in the inter-capillaryspace. This effect is caused by the higher resistance toflow of the non-woven mat, forcing the majority offluid flow through the inter-capillary spaces, whichhave a negligible flow resistance. This also causes theoverall pressure loss to be minimal. Since the samehydraulic permeability is used for the hepatocyte lay-ers, fluid velocities there are also in the range ofmicrometer per second. Consequently, apart from theincorporation of additional gas capillaries (case 10–11), also the presence of hepatocyte layers around thecapillaries (cell distribution 2) increased flow velocitiesand pressure loss in the model as the free cross-sec-tional area of the inter-capillary space is reduced. Fluidflow simulations for the inline and triangular variant ofthe different case studies render identical results forvelocity profiles, pressure loss and shear stress distri-butions. This was expected as the micro models consistof the identical geometrical entities, which are onlychanged in location relative to each other. From a fluiddynamical point of view, we conclude that the changein capillary arrangement along the course of the spiralmat in the AMC-BAL does not influence fluid flow,pressure drop or shear stress distribution.

The static pressure loss over one micro model can beregarded as the total pressure drop over the entireAMC-BAL without the inflow and outflow zone(Fig. 1e–g), since the AMC-BAL can be represented by300 micro models in parallel. This pressure drop, i.e.max. 200 Pa� 1.5 mmHg, is negligible when com-pared to the pressure losses in the extracorporeal cir-cuit. These low pressure gradients are in accordancewith the in vivo situation in the liver lobule, in whichpressure drops of approximately 3 mmHg over thesinusoids are normal.7,28 This is considered advanta-geous for cell culture inside the AMC-BAL.

Shear stress was also assessed as it is a possibledeterminant of cellular damage and reduced metabolicfunction. Shear stress is directly proportional to the

Improving Performance of the AMC-BAL Using CFD 1739

local velocity gradient and the fluid viscosity. Conse-quently, shear stresses are generally more elevated incases with higher velocity magnitudes in the inter-capillary space (e.g. in case of increased flow rate,doubled number of capillaries, cell distribution 2) andwhere fluid viscosity is increased (e.g. when plasma wasused instead of culture medium – ,clinical setting’ –case 12–13). Results show that only hepatocyteslocated at the side of the mat and at the border of thehepatocyte layers with the inter-capillary space aresubjected to a certain level of shear stress.

In vivo values of hepatocyte wall shear stress aredifficult to obtain, and comparison is therefore diffi-cult. In human, liver sinusoid wall shear stress s can becalculated as s ¼ Dp �D=4L� 1Pa (with static pressuredrop Dp� 3 mmHg; sinusoid diameter D� 9 lm;length L� 1 mm;7,28 and considering laminar flow anda cylindrical shape of the sinusoid). In mice sinusoids,shear stress was calculated to be 0.55 Pa.24,27 However,in vivo, hepatocytes are not directly subjected to thisshear stress as they are shielded by the sinusoidendothelial lining. As a result, the maximal tolerablelevel of shear stress is lower than 1 Pa. Tilles et al.38

showed in in vitro studies on rat hepatocytes thathepatocyte function, measured as albumin and ureasynthesis rates, was significantly decreased (resp. 2.6-and 1.9-fold) when hepatocytes were directly exposedto shear stresses higher than 0.5 Pa compared to lowshear stresses (<0.033 Pa). Under standard condi-tions, maximum shear stress values in the AMC-BALdo not exceed 0.04 Pa. Additionally, the majority ofthe hepatocytes are not subjected to significant shearstresses. Small zones with increased shear stress existbut maximal values are considered to be acceptableand not detrimental for the viability and function ofhepatocytes. However, shear stresses may increase upto 0.4 Pa when flow rate is increased 10-fold (case 9).Moreover, should plasma be used in this case, insteadof culture medium, maximal shear stress values maythen reach up to 0.71 Pa (not simulated; obtained bydata extrapolation), which is in the critical range(>0.5 Pa38). Additionally, very high flow rates, e.g. 10-times the normal culture flow rates, may causedetachment of hepatocytes and therefore should not beused in spite of any possible increase in local O2

availability. Subsequently, case 9 (culture medium flowrate� 10) can already be discarded in the search foroptimal O2 availability, based on fluid dynamicalgrounds.

Oxygen Transport and Consumption

We assessed the oxygen availability in different casestudies and in different micro model configurations. Inthis paragraph, the results are discussed per case.

Reference Case Simulations (Case 1)

Highest oxygen concentrations in the mat zone arelocated near the gas capillaries and near the border ofthe mat and the inter-capillary space. In zones withlimited flow velocities, cellular oxygen supply is clearlydependent on diffusion, which causes large radial pO2

gradients. On the other hand, diffusive O2 transportfrom the culture medium towards the hepatocytes alsocauses an axial gradient in culture medium oxygencontent. As a consequence, culture medium only oxy-genates the mat near the very start of the first matsegment and near the side of the mat. The depth of O2

penetration into the mat decreases rapidly furtherdownstream, since as the majority of oxygen content inthe convective flow is already consumed in the firstpart of the micro model. Nevertheless, oxygen level inthe culture medium is not totally depleted at the end ofthe micro model as the fluid transit time is not suffi-ciently long for all oxygen to diffuse to the hepato-cytes.

In contrast, the O2 concentration in the gas capil-laries remains constant along the micro model axis, sothe zone around the capillaries, which is oxygenatedhas a constant radius throughout the entire micromodel. This pattern of oxygenation leads to about 80%higher Vratio percentages in hepatocyte distribution 2as compared to 1, since more hepatocytes are close tothe gas capillaries in cell distribution 2. So despitesteeper pO2 gradients near the gas capillaries andconsequently a larger zone of depleted oxygen in themat zone in case of hepatocyte distribution 2, this celldistribution leads to significantly higher Vratio per-centages. However, this effect is related to the maximaloxygen diffusion distance, which is limited by theMichaelis–Menten oxygen consumption parameters,local hepatocyte density and local diffusion coefficientin general and by the specific local gas capillary andculture medium pO2 in this reference case.

Since regions which are oxygenated by one gascapillary in particular do not overlap or influence eachother in the reference case simulations, diffusive oxy-gen supply by the capillaries is independent of relativecapillary location. Convective oxygen transport is alsoidentical as flow distribution is irrespective of capillaryplacement (section ‘‘Fluid flow and shear stress dis-tribution’’). Consequently, inline and triangular capil-lary pattern give identical results concerning oxygentransport and consumption in these reference caseswhen the same hepatocyte distribution is used, as isconfirmed by simulation results.

Concerning oxygen transport, we can conclude thatthe oxygen supply in the AMC-BAL is not fully ade-quate to provide all hepatocytes with sufficient oxygento maintain O2 consumption at minimally 90% of the

MAREELS et al.1740

maximal uptake rate (Vratio>0.9). Given that theAMC-BAL can be modeled as a combination of micromodel configurations, 16–28% of the hepatocytes inthe AMC-BAL are adequately oxygenated. In otherwords, between 72% and 84% of the hepatocytes aresubjected to a pO2 of less than 18 mmHg under thecurrent conditions. Normal physiological pO2 values inthe liver sinusoids are between 70 mmHg in the peri-portal area and 20 mmHg in the pericentral area.42 Butit is difficult to determine the effect on viability andfunction of hepatocytes below this threshold. Studiesindicate that hepatocyte respiration becomes impairedbelow 1–2 mmHg pO2.

10 With respect to these values,further investigation of simulation results showed thatunder current conditions 67% and 52% of the he-patocytes in cell distribution 1 and 2 have a pO2 below2 mmHg and will suffer from hypoxia. The remaining17–20% of the hepatocytes are likely to be character-ized by shifts to more anaerobic metabolic processes.36

However, it should be noted that the low‘‘Vratio>0.9’’ percentages are largely influenced by thevery stringent hepatocyte oxygen consumption ratiosused in this numerical model. Also, hepatocytes whichare subjected to low oxygen levels for a prolongedperiod of time might show changes in oxygen con-sumption characteristics (VM, KM) to compensate forthe lack of oxygen. This could account for account forhigher oxygen availability in vitro. The use of different(VM, KM)-values throughout the model to address thisbehavior can be implemented in future work. Never-theless, further increase in O2 availability may proveuseful to increase the cell viability and subsequently theefficiency of the AMC-BAL.

The Effect of the Internal Oxygenator (Case 2,3)

Disabling the internal oxygenator leads to detri-mental results and reduces the percentage of ade-quately oxygenated hepatocytes to virtually zero. Thisconfirms the importance of the internal oxygenatorand illustrates the small contribution of the incomingconvective oxygen flux by culture medium. Incomingculture medium flow adds only 0.17 nmol O2 per sec-ond to the micro model, while maximal oxygen uptakeVM equals 0.7286 nmol/s*106 cells. As such, theoreti-cally no more than 0.2� 106 cells, i.e. 6% of the totalamount of hepatocytes per micro model, would be ableto consume at maximal uptake rate. In reality, only1.7% of the hepatocytes can consume at a Vratio>0.9due to the presence of pO2 gradients. Replacing theinternal oxygenator by an external oxygenator, whichdoubles the flow pO2 and thus the convective oxygenflux, will only increase the ‘‘Vratio>0.9’’ percentage toabout 6%. Since this is still considerably less than in thereference cases, external oxygenation – even at elevated

pO2 levels – is a not suitable replacement for theinternal oxygenation system as the gas capillariesconstitute the main oxygen supply. As such, theinternal oxygenator is an essential part of the AMC-BAL.

Increasing Oxygen Availability (Case 4–11)

In the reference case models, merely 16–28% of thehepatocytes are adequately supplied with oxygen toconsume at a Vratio>0.9, depending on hepatocytedistribution. We therefore assessed several strategies toincrease overall oxygen availability.

Culture medium flow rate (case 8,9) does not have aconsiderable effect on cellular oxygen availability. A 2-fold increase in flow rate resulted in an increase inregions with Vratio>0.9 of only 14%. This was ex-pected as the convective oxygen supply is only a minorcontributor to the overall oxygen supply. Conse-quently, doubling the medium pO2 (case 6) does notgreatly increases the amount of regions with sufficientoxygen either. As already discussed, changes in culturemedium properties are reflected in a small increase ofregions with Vratio in the mat zone, and more specifi-cally in the first mat segment as oxygen content of thefluid is rapidly decreased downstream. It is interestingto note that doubling the flow rate and doubling themedium pO2 both supply exactly the same amount ofoxygen to the micro model: in the latter, oxygen issupplied at increased pO2, whereas in the former oxy-gen is supplied at standard level but with a higher flowrate. Nevertheless, doubling pO2 medium is preferredcompared to increasing flow rate when aiming at abetter effective hepatocyte utilization ratio since thedoubled flow rate does not give the oxygen enoughtime to diffuse to the hepatocytes as the residence timebefore oxygen exits the micro model is cut in half.However, a disadvantage of increasing pO2 in themedium is the requirement of an external oxygenator,which makes the extracorporeal circuit more complexand costly and increases the extracorporeal plasmavolume in a clinical setting.

Doubling the pO2 of the oxygenation gas (case 4) ismuch easier to achieve in practice. Importantly, the‘‘Vratio>0.9’’ percentage increases significantly to al-most a doubled level as compared to the reference case.In comparison, culture medium flow rate has to beincreased more than 10-fold (case 9) to achieve similarresults as with a 2-fold increase in pO2 of the oxygen-ation gas. This illustrates how oxygen supply is onlyminor dependent on fluid flow rate. However, satura-tion of ‘‘Vratio>0.9’’ percentages with increasedflow rate is not yet achieved at 10-fold flow rate.Nevertheless, a 10-fold flow rate is not preferredbecause of possible detachment of the hepatocytes and

Improving Performance of the AMC-BAL Using CFD 1741

an increased risk of possible shear stress damage to thehepatocytes.

The effective hepatocyte utilization ratio can even befurther improved. Culture medium pO2 can be set tocarbogen level (case 7) or the number of capillaries canbe doubled (case 10). On average and for both hepa-tocyte distributions, these two methods lead to a 2-foldincrease in the amount of hepatocytes consumingoxygen at Vratio>0.9 as compared to the referencecase. When both approaches are compared for hepa-tocyte distribution 1, the results are slightly betterwhen using the carbogen medium pO2. But for hepa-tocyte distribution 2, the double number of capillariesleads to better results. An increase in the number ofcapillaries is preferred over carbogen medium perfu-sion, since carbogen medium perfusion leads to ex-tremely high and possible toxic12 pO2 values of almost720 mmHg. Carbogen medium perfusion also requiresan additional external oxygenator. Therefore, increas-ing the number of capillaries by 2-fold is a more easyand safe method to increase the effective hepatocyteutilization ratio.

The results obtained with double capillary numbersare also better when compared to the doubling of theoxygenation gas pO2. In cell distribution 2, this ismainly caused by the redistribution of the hepatocyteslocated around the capillaries. By increasing thenumber of capillaries, the hepatocyte layer thicknessdecreased (section ‘‘Modeling oxygen transport andconsumption’’). As a consequence, the region that agas capillary can sufficiently oxygenate now spans theentire hepatocyte layer so 100% of the cell layer(Table 4) is sufficiently oxygenated. In cell distribution1, the total region with Vratio>0.9 has also increasedby two, as each additional capillary supplies an addi-tional (constant) volume of hepatocytes withVratio>0.9. In contrast, doubling the oxygenation gaspO2 increases the region surrounding a single capillarywith Vratio>0.9 with a factor of less than two.

The ultimate results in improving cellular oxygenavailability and effective hepatocyte utilization ratioare found when oxygenation gas is set to carbogenlevel (case 5) or when a double number of capillaries isused in combination with a doubled oxygenation gaspO2 (case 11). Vratio>0.9 percentages have quadru-pled for cell distribution 1 and tripled for cell distri-bution 2 as compared to the reference case for bothapproaches.

Simulation results show that in case 11, the respec-tive gains in Vratio>0.9 regions are cumulated whenthe case of a double number of capillaries and a dou-bled pO2 gas are combined. It can also be noted thatthere is a small but significant difference between theinline and triangular capillary pattern in case 5. Whencarbogen oxygenation gas is used, the region with

Vratio>0.9 surrounding a capillary has grown to suchan extent that it could overlap with the region of sur-rounding capillaries. If a capillary is present straightopposed to another (inline pattern), this overlap ispresent. Consequently, the intersection of the two re-gions only contributes once to the amount of regionwith Vratio>0.9. In contrast, when capillaries are in atriangular pattern, the region surrounding the capillarycan extent to its fullest, thus increasing the percentageVratio>0.9 more compared to the inline micro model.This effect is more pronounced in the cell distribution 2compared to distribution 1.

Given the possible toxicity of the hyperoxic oxygenlevels when carbogen oxygenation gas is used (case 5),the preferred method to optimally and maximallyincrease oxygen availability in the AMC-BAL is todouble the number of gas capillaries together with a2-fold increase in culture gas pO2. We note, however,that the calculated improvements in O2 availability andVratio>0.9 percentages do not necessarily translateinto identical increases in cell viability or functionalactivity. Nevertheless, similar trends between simula-tion results and the in vitro situation are expected, buthave to be validated.

Clinical Versus Experimental Setting (Case 12,13)

An important 20–25% decrease in the amount ofhepatocytes with Vratio>0.9 is caused by the lowerdiffusion coefficient ()9%) and oxygen solubility()25%) in plasma as compared to culture medium. Asin reference case 1, results are independent of capillarypattern and are higher in cell distribution 2 as com-pared to cell distribution 1. Doubling the oxygenationgas pO2 in the clinical setting leads to approximatelythe same relative increase in Vratio percentages as itdoes in the experimental setting. As such, we concludethat any relative increase in oxygen availability foundin the experimental setting by any possible strategy canalso be applied to the clinical setting, taking intoaccount that the absolute Vratio>0.9 fractions aredecreased with a constant percentage depending onhepatocyte distribution.

Changes in Hepatocyte O2 Consumption in Time (Case14,15)

Higher KM values of day 4 and 5 cause the decreasein oxygen consumption to start at higher oxygen levelscompared to lower KM values of day 2. Consequently,pO2 gradients are less steep and oxygen penetratesfurther into the mat zone or into hepatocyte layersbecause of the reduced local O2 uptake. Paradoxically,‘‘Vratio>0.9’’ fractions have decreased. This isunderstood when converting the Vratio threshold to theminimal cellular pO2 to which the hepatocytes must be

MAREELS et al.1742

subjected to, using Eq. 4. Whereas in the referencecase, hepatocytes are considered to be sufficientlyoxygenated when cellular pO2 reaches at least18 mmHg, threshold values are now approximately 43and 68 mmHg for day 4 and 5, respectively. Since theoverall pO2 level in the latter cases is not equally ele-vated, Vratio>0.9 fractions are strongly reduced.Conversely, when applying an identical pO2 thresholdinstead of Vratio, hepatocyte percentages in case 14 and15 are increased with 3% and up to 20% compared today 2. As such, an increase in KM causes average cel-lular pO2 to increase, but whether there is also an in-crease in the number of hepatocytes that aresufficiently oxygenated is difficult to determine basedon computer simulations, as this depends on thecriteria, i.e. minimal Vratio versus minimal pO2, used.

CONCLUSIONS

A numerical model to investigate fluid flow andoxygen transport and consumption in the AMC-BALwas developed and applied to two representative micromodels of the AMC-BAL. Two different gas capillarypatterns, i.e. ,inline’ and ,triangular’, were used andcombined with two proposed hepatocyte distributions,leading to four basic configurations in total. Fifteencase studies were performed on each of the configu-rations in order to gain insight in the fluid flow, shearstress distribution, oxygen availability and effectivehepatocyte utilization ratio Vratio of the AMC-BALand to assess possible strategies to further improvecellular oxygen availability. We found that the AMC-BAL does not provide sufficient oxygen to all he-patocytes to allow them to consume oxygen at 90% oftheir maximal uptake rate under standard operatingconditions. The internal oxygenator is an essential partof the AMC-BAL. Doubling the number of gas cap-illaries together with a 2-fold increase in the oxygena-tion gas pO2 was found to be the optimal method tomaximally increase O2 availability. Additionally,pressure drop over the AMC-BAL and cellular shearstress levels were found to be low and advantageous tocell culture. The developed model also allowed us toassess the effect of the transition from the in vitro to theclinical setting and the effect of the change of hepa-tocyte O2 consumption characteristics in time. Sincelarge variations in simulation results between hepato-cyte distributions are shown, an assessment of the invitro hepatocyte distribution in the AMC-BAL is use-ful. Subsequently, an attempt to validate the numericalmodel with in vitro experiments should be made.Eventually, adoption of this information may lead to amore efficient and productive AMC-BAL in the nearfuture.

ACKNOWLEDGMENTS

First author’s research is supported by a BOF-grant(011D09503) from Ghent University, Belgium. Theauthors also express their gratitude to the NetherlandsDigestive Diseases Foundation (MLDS), the Tech-nology Foundation of NWO (The Netherlands), andthe European Union (QLTR-2000-01889) for financialsupport.

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